The European Commission says "ambitious steps" to turn the eurozone into a full banking union are required if stability is going to be restored. Leaders will discuss the plan at their June summit.
Megan Greene, eurozone economist at Roubini Global Economics, believes an EU wide banking union "would be a big step" but she does not think its "politically feasible".
"There is no way [EU leaders] will agree to it and certainly not by June" she told the Today programme.
Business editor Robert Peston said that, while it may not happen immediately, "more or less all businesses, bankers and... senior members of the government are assuming that Greece will leave the euro".
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